Clifford algebras, algebraic spinors, quantum information and applications

Abstract

We give an algebraic formulation based on Clifford algebras and algebraic spinors for quantum information. In this context, logic gates and concepts such as chirality, charge conjugation, parity and time reversal are introduced and explored in connection with states of qubits. Supersymmetry and M-superalgebra are also analysed with our formalism. Specifically we use extensively the algebras $C{l}_{3,0}$ and $C{l}_{1,3}$ as well as tensor products of Clifford algebras.